In this chapter the emphasis will be on the “Andronov-Hopf bifurcation”, the generic mathematical model of the phenomenon how a real world system depending on a parameter is losing the stability of an equilibrium state as the parameter is varied, giving rise to small stable or unstable oscillations. This will be treated in Section 2; applications in population dynamics will be presented in Sections 3 and 4. In Section 1 the underlying theory of structural stability will be dealt with in a concise form. According to the general structure of this book this Section ought to go into the Appendix; however, in this last chapter it yields, probably, an easier reference standing at the start.
KeywordsPeriodic Solution Periodic Orbit Equilibrium Point Homoclinic Orbit Centre Manifold
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